Twin primes and prime bunches in mathematicians’ crosshairs

Major advance made toward proving difficult conjecture

A famous conjecture in number theory has stood unproven for more than 150 years, but for the second time this year, mathematicians have gotten dramatically closer to proving it. With a strategy others had abandoned, a young mathematician has narrowed the gap between primes, in hopes of ultimately proving the twin prime conjecture. His work has also shown that prime numbers bunch together in clusters as well as in pairs.

The twin prime conjecture asserts that infinitely many pairs of prime numbers are separated by only two, as are 3 and 5 or 1997 and 1999. Prime numbers are divisible only by themselves and 1. Number theorists know that as numbers get larger, primes gradually get sparser. Nonetheless, if the twin prime conjecture is true, pairs of primes spaced as closely together as possible continue to pop up forever.

Number theorists have been revved up since May, when Yitang “Tom” Zhang, a University of New Hampshire mathematician, announced a partial

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